import pylab from numpy import asarray from lorenz import Lorenz l = Lorenz(10.0, 28.0, 8.0/3.0) dtraj, traj = [], [] DT, NSTEP = 0.01, 1000 dx, dy, dz = 0.0, 10.0, 10.0 x, y, z = 0.0, 10.0, 10.0 dtraj.append((dx, dy, dz)) traj.append((x, y, z)) for i in range(NSTEP): dx, dy, dz = l.diff(x, y, z, dx, dy, dz, DT) x, y, z = l.step(x, y, z, DT) dtraj.append((dx, dy, dz)) traj.append((x, y, z)) trajadj = [] xadj, yadj, zadj = 0.0, 10.0, 10.0 trajadj.append((xadj, yadj, zadj)) for i in range(NSTEP-1, 0-1, -1): x, y, z = traj[i] xadj, yadj, zadj = l.adj(x, y, z, xadj, yadj, zadj, DT) trajadj.append((xadj, yadj, zadj)) trajadj.reverse() aggr = (asarray(trajadj) * asarray(dtraj)).sum(axis=1) # pylab.plot(aggr)
delta = 0.1
deltas = []
grads = []
for i in range(5):
dtraj = []
traj0 = []
traj1 = []
dx, dy, dz = 0.0, 10.0, 10.0
x0, y0, z0 = 0.0, 10.0, 10.0
x1, y1, z1 = x0 + delta * dx, y0 + delta * dy, z0 + delta * dz
dtraj.append((dx, dy, dz))
traj0.append((x0, y0, z0))
traj1.append((x1, y1, z1))
for i in range(NSTEP):
dx, dy, dz = l.diff(x0, y0, z0, dx, dy, dz, DT)
x0, y0, z0 = l.step(x0, y0, z0, DT)
x1, y1, z1 = l.step(x1, y1, z1, DT)
dtraj.append((dx, dy, dz))
traj0.append((x0, y0, z0))
traj1.append((x1, y1, z1))
grad = (asarray(traj1[-1]) - asarray(traj0[-1])) / asarray(dtraj[-1])
deltas.append(delta); grads.append(grad)
delta *= 0.1
deltas, grads = asarray(deltas), asarray(grads)
pylab.loglog(deltas, grads[:,0],'+-')
pylab.loglog(deltas, grads[:,1],'+-')
pylab.loglog(deltas, grads[:,2],'+-')
